Bayesian inference is common in models with many parameters, such as large VAR models, models with time-varying parameters, or large DSGE models. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters. The choice of these hyperparameters is crucial because their influence is often sizeable for standard sample sizes. In this paper we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model.
In terms of applications, we show via Monte Carlo simulations that in time series models with time-varying parameters and stochastic volatility, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature.